Modeling Beer Price Development Over the Years

Note: The currency used in the data is €. All prices before the year 2002 have been transformed from DM (German currency before 2002) to Euro.

In fact, the price for 1L beer increased almost linear over the years. We will try to use a simple linear regression model to describe the data:

fit_beer <- lm(beer_price ~ year, data = dt)
summary(fit_beer)

## 
## Call:
## lm(formula = beer_price ~ year, data = dt)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.44439 -0.13266  0.00188  0.14010  0.55504 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -4.886e+02  8.710e+00  -56.09   <2e-16 ***
## year         2.475e-01  4.352e-03   56.87   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2489 on 32 degrees of freedom
## Multiple R-squared:  0.9902, Adjusted R-squared:  0.9899 
## F-statistic:  3234 on 1 and 32 DF,  p-value: < 2.2e-16

Our model suggests that the beer price increased by 0.25 Euro per year.

Fitting models to the years with different currencies separately, we see a small difference in estimated price increase per year:

fit_dm <- lm(beer_price ~ year, data = subset(dt, year < 2002))
summary(fit_dm)

## 
## Call:
## lm(formula = beer_price ~ year, data = subset(dt, year < 2002))
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.236176 -0.112059 -0.009412  0.077647  0.260000 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -4.203e+02  1.399e+01  -30.04 8.17e-15 ***
## year         2.132e-01  7.022e-03   30.37 6.94e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1418 on 15 degrees of freedom
## Multiple R-squared:  0.984,  Adjusted R-squared:  0.9829 
## F-statistic: 922.2 on 1 and 15 DF,  p-value: 6.944e-15

fit_euro <- lm(beer_price ~ year, data = subset(dt, year >= 2002))
summary(fit_euro)

## 
## Call:
## lm(formula = beer_price ~ year, data = subset(dt, year >= 2002))
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.20382 -0.02073 -0.01728  0.01625  0.31294 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -5.875e+02  1.148e+01  -51.18   <2e-16 ***
## year         2.967e-01  5.711e-03   51.95   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1154 on 15 degrees of freedom
## Multiple R-squared:  0.9945, Adjusted R-squared:  0.9941 
## F-statistic:  2699 on 1 and 15 DF,  p-value: < 2.2e-16

• In years with DM currency (1985 to 2001) the estimated yearly price increase was around 0.21 Euro per year.
• In the years after the Euro has been introduced (>2001), the estimated yearly price increase was 0.3 Euro per year.

Influence of Beer Price on Consumption

Now that we confirmed that the price increased over the years, the next question which arises is:

Did this increase have a negative influence on mean beer consumption per visitor?

In order to answer this question we are going to start with a visualization of our data:

We do not see a decline in mean beer consumption per visitor over the years. In fact, since around year 1999 it seems that it even has been increasing steadily.

To see how the data are correlated we perform a correlation test using the Pearson correlation coefficient:

cor.test(dt$beer_cons_per_visitor, dt$beer_price)

## 
##  Pearson's product-moment correlation
## 
## data:  dt$beer_cons_per_visitor and dt$beer_price
## t = 17.106, df = 32, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.9003351 0.9746671
## sample estimates:
##       cor 
## 0.9494338

The test suggests a true correlation with a Pearson correlation coefficient of 0.95. The p-value is way below 0.05 and we have a narrow confidence interval. If we plot the data, all points seem to be around one line:

This result would suggest that beer consumption increases the higher the beer price gets. Nevertheless, in my opinion, this is an example that correlation does not imply causation. I think that the increased consumption is a separate phenomena and not caused by increased prices. One reason you can think of might be:

• Oktoberfest gets more and more popular outside of Munich. More and more people from all over the world go there in order to drink a “Maß” beer. For people coming from Australia, Sweden, etc. the beer is still cheap compared to their home. That is why they do not consume less beer with increasing prices since it is still cheap for them.

In conclusion the data set suggests that the price does not seem to have a negative influence on mean beer consumption per visitor.

Modeling Hendl Price Development

As before we are going to have a look at the price only first:

Important Notes:

1. The currency used in the data is €. All prices before the year 2002 have been transformed from DM (German currency before 2002) to Euro.
   
2. Before the year 2000 the data are mean prices at the selling places. Since 2000 the data are only mean prices inside the tents.

It seems that there was a huge price increase in year 2000. But we need to be careful: As mentioned in the notes above, the data collection method changed in 2000. So we need to compare both periods separately. In the year 2013 we have some kind of price outlier. Here the price was raised a huge amount compared to the steady increase the years before. After that, the price dropped to a level which seems to lie on a line of steady price increase. We will try to model the price increase from year 2000 on using a linear regression model.

fit_hendl <- lm(hendl_price ~ year, data = subset(dt, year >= 2000))
summary(fit_hendl)

## 
## Call:
## lm(formula = hendl_price ~ year, data = subset(dt, year >= 2000))
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.33063 -0.14774 -0.08568  0.15142  0.72347 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -434.17863   23.20885  -18.71 8.89e-13 ***
## year           0.22084    0.01155   19.12 6.25e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2758 on 17 degrees of freedom
## Multiple R-squared:  0.9555, Adjusted R-squared:  0.9529 
## F-statistic: 365.4 on 1 and 17 DF,  p-value: 6.254e-13

The model suggests that the hendl price increased by 0.22 Euro per year since 2000.

When we add the model to our plot it looks like this:

Influence of Hendl Price on Consumption

Above we saw that the beer price did not have a negative influence on the beer consumption. We are going to ask the same question for the hendl price and consumption. To get a first overview, we plot the data.

We see that the hendl consumption dropped in 2001 after slowly decreasing from 1991 on. After the drop, the consumption stayed at a constant level, whereas the price went up.
For me it looks like the hendl consumption being correlated with price until year 2000. After that the consumption reached a minimum bound. Maybe at this point price sensitivity of the remaining hendl consumers changes.

We can check the correlation by performing a correlation test using the Pearson correlation coefficient:

with(subset(dt, year < 2000),cor.test(hendl_cons_per_visitor*100, hendl_price))

## 
##  Pearson's product-moment correlation
## 
## data:  hendl_cons_per_visitor * 100 and hendl_price
## t = -2.1586, df = 13, p-value = 0.05016
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.812214934 -0.001917789
## sample estimates:
##       cor 
## -0.513676

with(subset(dt, year >= 2000),cor.test(hendl_cons_per_visitor*100, hendl_price))

## 
##  Pearson's product-moment correlation
## 
## data:  hendl_cons_per_visitor * 100 and hendl_price
## t = -1.4261, df = 17, p-value = 0.1719
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.6801148  0.1495249
## sample estimates:
##       cor 
## -0.326885

The correlation coefficients suggest a negative correlation for both periods. Nevertheless, the tests confirm the null hypothesis, which says that there is no true correlation between the variables.

For the period before 2000 there is at least a strong tendency (p = 0.0501576) for a true negative correlation. Despite that, the confidence interval for the correlation coefficient is very big, which gives us a strong uncertainty.

In conclusion we can say that the price seems to have an influence on the hendl consumption up to a specific point. Maybe we could explain the constant level of consumption after reaching that specific price margin with the following hypothesis:

Normally people would buy a hendl up to their specific price boundary. That would mean a steady decrease in consumption with increasing price.

Nevertheless, there are a lot of companies, which rent a table in a tent and invite their employees to come. Most of the time these companies give a free amount of hendl and beer consumption to their employees. I think that a big company’s price sensitivity concerning hendl and beer is not as high as the price sensitivity of a normal Oktoberfest visitor. Thus, even with increasing prices the basic level of consumption does not change a lot.